Ball Rise Trajectory: How Fast Was the Ball Moving?

In summary, to find the speed of the ball when it left the racket, we need to solve for v in two equations: one relating the horizontal motion of the ball to its position at the net, and another relating the vertical motion of the ball to the height it needs to clear the net. Once we solve for v in both equations, we can find the speed of the ball using the formula v=sqrt(vx^2+vy^2).
  • #1
UrbanXrisis
1,196
1
A tennis player standing 12.6 m from the net hits the ball at 3 degrees above the hoizontal. To clear the net, the ball must rise at lease 0.33m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racket?

would it just be sqrt(12.6^2+0.33^2) ?
 
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  • #2
no. find an equation relating the horizontal motion of the ball, to reach the net. find another equation relating the vertical motion of the ball to clear the net. solve the equations for v.
 
  • #3
they do not specify time so I could have 12.6m/s ins the x direction and .33m/s in the y direction

hence:
v=sqrt(12.6^2+0.33^2)
 
  • #4
Origin : the player's position.
Horizontal motion :
s=ut
12.6=(vcos3)*t
Vertical motion :
[tex]0.33=t*vsin3-\frac{g}{2}t^2[/tex]
Solve the equations for v.
 

1. What is ball rise trajectory?

Ball rise trajectory is the path that a ball takes as it is thrown or launched into the air. It is affected by factors such as the initial speed and angle of launch, gravity, and air resistance.

2. How is the speed of the ball calculated?

The speed of the ball can be calculated by using the equation: speed = distance/time. This means that the distance the ball travels in a certain amount of time is divided by that time to determine its speed.

3. How does the angle of launch affect the ball rise trajectory?

The angle of launch can greatly affect the ball rise trajectory. A higher angle will result in a steeper trajectory, while a lower angle will result in a flatter trajectory. The angle also affects the distance the ball travels and the time it takes to reach its peak height.

4. What factors can affect the speed of the ball?

The speed of the ball can be affected by various factors such as the initial force applied to the ball, air resistance, and gravity. Other factors such as the surface the ball is launched from and the air temperature can also have an impact on the speed.

5. How can the ball rise trajectory be predicted?

The ball rise trajectory can be predicted by considering the initial speed and angle of launch, as well as the external factors such as gravity and air resistance. Using mathematical equations and calculations, the predicted trajectory can be determined. However, slight variations in these factors can affect the actual trajectory of the ball.

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